The radius of the base of a right circular cone is 6 and the radius of a parallel cross section is 4. If the distance between the base and the cross section is 8, what is the height of the cone?
[see the figure attached] Let's take a look at a vertical section of the cone. By Thales' theorem, the height is \(\dfrac{BD}{CE}=\dfrac{AB}{AC}\) hence \(h=AC=\dfrac{AB\cdot CE}{BD}=\dfrac{(h-8)\cdot6}{4}\) thus \(\boxed{h=24}\)
